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1020World and LogicCollege Publications. 2021.What is the relationship between the world and logic, between intuition and language, between objects and their quantitative determinations? Rationalists, on the one hand, hold that the world is structured in a rational way. Representationalists, on the other hand, assume that language, logic, and mathematics are only the means to order and describe the intuitively given world. In World and Logic, Jens Lemanski takes up three surprising arguments from Arthur Schopenhauer’s hitherto undiscovered …Read more
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634Schopenhauers Gebrauchstheorie der Bedeutung und das Kontextprinzip: Eine Parallele zu Wittgensteins ›Philosophischen Untersuchungen‹Schopenhauer Jahrbuch 2016 (97): 171-195. 2016.In previous research, Schopenhauer is regarded as a consistent representative of a classical picture theory of language. The paper shows, however, that Schopenhauer does not only present a use theory of meaning in his lectures on logic, but also justifies it with the help of the context principle. Furthermore, it is discussed to what extent Schopenhauer's use theory of meaning is similar to the semantic theory of Ludwig Wittgenstein and his successors.
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552Periods in the Use of Euler-type DiagramsActa Baltica Historiae Et Philosophiae Scientiarum 5 (1): 50-69. 2017.Logicians commonly speak in a relatively undifferentiated way about pre-euler diagrams. The thesis of this paper, however, is that there were three periods in the early modern era in which euler-type diagrams (line diagrams as well as circle diagrams) were expansively used. Expansive periods are characterized by continuity, and regressive periods by discontinuity: While on the one hand an ongoing awareness of the use of euler-type diagrams …Read more
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480Reism, Concretism and Schopenhauer DiagramsStudia Humana 9 (3/4): 104-119. 2020.Reism or concretism are the labels for a position in ontology and semantics that is represented by various philosophers. As Kazimierz Ajdukiewicz and Jan Woleński have shown, there are two dimensions with which the abstract expression of reism can be made concrete: The ontological dimension of reism says that only things exist; the semantic dimension of reism says that all concepts must be reduced to concrete terms in order to be meaningful. In this paper we argue for the following two theses: (…Read more
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465Logikdiagramme und Logikmaschinen aus der Zittauer Schule um Christian WeiseNeues Lausitzische Magazin 141 (1): 39-57. 2019.A particularly promising trail on the search for forgotten logic diagrams leads to Upper Lusatia in the 17th century, more precisely to Christian Weise and his students. Samuel Grosser, who later became rector in Görlitz, and Johann Christian Lange, who later became professor of logic at the University of Gießen, are the most prominent to have published remarkable logic diagrams. Even more remarkable, however, is the fact that Lange's interest in these diagrams ultimately gave rise to the idea o…Read more
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455Means or end? On the Valuation of Logic DiagramsLogic-Philosophical Studies 14 98-122. 2016.From the beginning of the 16th century to the end of the 18th century, there were not less than ten philosophers who focused extensively on Venn’s ostensible analytical diagrams, as noted by modern historians of logic (Venn, Gardner, Baron, Coumet et al.). But what was the reason for early modern philosophers to use logic or analytical diagrams? Among modern historians of logic one can find two theses which are closely connected to each other: M. Gardner states that since the Middle Ages certain…Read more
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451Techniques of Bridging the Gulf: Dialectic and Reductionism in McDowell and FichteEdukacja Filozoficzna 69 (1): 7-36. 2020.“Dialectic” has been a matter of growing interest in contemporary philosophy. The present article analyzes dialectical methods and positions them by reference to two paradigmatic texts of German idealism and analytic philosophy, i.e. J.G. Fichte’s Science of Knowing (1804) and J. McDowell’s Mind and World. Both dialectical approaches will be interpreted with regard to their contribution in the debate on reductionism and anti-reductionism: both Fichte and McDowell claim that philosophical positi…Read more
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396Logic Diagrams as Argument Maps in Eristic DialecticsArgumentation 37 (1): 69-89. 2023.This paper analyses a hitherto unknown technique of using logic diagrams to create argument maps in eristic dialectics. The method was invented in the 1810s and -20s by Arthur Schopenhauer, who is considered the originator of modern eristic. This technique of Schopenhauer could be interesting for several branches of research in the field of argumentation: Firstly, for the field of argument mapping, since here a hitherto unknown diagrammatic technique is shown in order to visualise possible situa…Read more
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378Discourse Ethics and EristicPolish Journal of Aesthetics 62 151-162. 2021.Eristic has been studied more and more intensively in recent years in philosophy, law, communication theory, logic, proof theory, and A.I. Nevertheless, the modern origins of eristic, which almost all current researchers see in the philosopher Arthur Schopenhauer, are considered to be a theory of the illegitimate use of logical and rhetorical devices. Thus, eristic seems to violate the norms of discourse ethics. In this paper, I argue that this interpretation of eristic is based on prejudices th…Read more
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353Analyzing the philosophy of travel with Schopenhauerian argument mapsSouthern Journal of Philosophy 61 (4): 588-606. 2023.Emily Thomas's seminal book The Meaning of Travel has brought the philosophy of travel back into the public eye in recent years. Thomas has shown that the topic of travel can be approached from numerous different perspectives, ranging from the historical to the conceptual‐analytical, to the political or even social‐philosophical perspectives. This article introduces another perspective, which Thomas only indirectly addresses, namely the argumentation‐theoretical perspective. It is notable that c…Read more
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332Schopenhauer's World. The System of The World as Will and Presentation ISchopenhaueriana. Revista Española de Estudios Sobre Schopenhauer 2. 2017.in recent years, the research on Schopenhauer has shown a change in the interpretation of his main work, «The World as Will and Presentation», from (1) a normative and linear instruction which guides the reader from idealism to mysticism, pessimism and nothingness to (2) value-free and independent descriptions of the world with all phenomena (like idealism, mysticism, nothingness etc.) in it. thus Schopenhauer’s main work has become an empirical or baconian approach—something like a «philosophic…Read more
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330Kant’s Crucial Contribution to Euler DiagramsJournal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 55 (1). 2024.Logic diagrams have been increasingly studied and applied for a few decades, not only in logic, but also in many other fields of science. The history of logic diagrams is an important subject, as many current systems and applications of logic diagrams are based on historical predecessors. While traditional histories of logic diagrams cite pioneers such as Leibniz, Euler, Venn, and Peirce, it is not widely known that Kant and the early Kantians in Germany and England played a crucial role in popu…Read more
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309Die ›Evolutionstheorien‹ Goethes und Schopenhauers. Eine kritische Aufarbeitung des wissenschaftsgeschichtlichen ForschungsstandesIn Daniel Schubbe & Søren Fauth (eds.), Schopenhauer und Goethe: Biographische und philosophische Perspektiven, Meiner. pp. 247-299. 2016.This article compares the research literature published by Goethe and Schopenhauer on the subject of evolutionary theory. The metatheoretical thesis is supported that the results of any comparison between Schopenhauer or Goethe and a concrete theory of evolution always depend on three dimensions: 1. the scientific point of view of the comparative, 2. the meaning and definition of the central terms and 3. the selection of the analyzed primary literature. It is also argued that no previously publi…Read more
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305Fichte’s Formal LogicSynthese 202 (1): 1-27. 2023.Fichte’s Foundations of the Entire Wissenschaftslehre 1794 is one of the most fundamental books in classical German philosophy. The use of laws of thought to establish foundational principles of transcendental philosophy was groundbreaking in the late eighteenth and early nineteenth century and is still crucial for many areas of theoretical philosophy and logic in general today. Nevertheless, contemporaries have already noted that Fichte’s derivation of foundational principles from the law of id…Read more
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303Transcendental Philosophy and Logic DiagramsPhilosophical Investigations 1-27. forthcoming.Logic diagrams have seen a resurgence in their application in a range of fields, including logic, biology, media science, computer science and philosophy. Consequently, understanding the history and philosophy of these diagrams has become crucial. As many current diagrammatic systems in logic are based on ideas that originated in the 18th and 19th centuries, it is important to consider what motivated the use of logic diagrams in the past and whether these reasons are still valid today. This pape…Read more
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301›Cur potius aliquid quam nihil‹ von der Frühgeschichte bis zur HochscholastikIn Daniel Schubbe, Jens Lemanski & Rico Hauswald (eds.), Warum ist überhaupt etwas und nicht nichts? Wandel und Variationen einer Frage, Meiner. 2013.Inspired by various research results on the history of philosophy that have not yet been compiled, the paper pursues the thesis that the question "Why is there something rather than nothing" was formulated long before Leibniz. In reviewing this thesis, the 'fundamental question' is differentiated into two individual questions: "Why is there something at all" and 'Why isn't rather nothing?". On the basis of this systematic distinction, the paper examines the history of philosophy from early histo…Read more
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278Combing Graphs and Eulerian Diagrams in EristicIn Valeria Giardino, Sven Linker, Tony Burns, Francesco Bellucci, J. M. Boucheix & Diego Viana (eds.), Diagrammatic Representation and Inference. 13th International Conference, Diagrams 2022, Rome, Italy, September 14–16, 2022, Proceedings, Springer. 2022.In this paper, we analyze and discuss Schopenhauer’s n-term diagrams for eristic dialectics from a graph-theoretical perspective. Unlike logic, eristic dialectics does not examine the validity of an isolated argument, but the progression and persuasiveness of an argument in the context of a dialogue or even controversy. To represent these dialogue situations, Schopenhauer created large maps with concepts and Euler-type diagrams, which from today’s perspective are a specific form of graphs. We fi…Read more
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253Von Brucker zu Augustinus: Probleme mit der Geschichte des Begriffs >NeuplatonismusArchiv für Begriffsgeschichte 53 33-53. 2011.Normally in nowadays philosophical research the term 'Neoplatonism' is coined and it was used the first time by Jacob Brucker in the first half of the 18th century. But there are signs that the concept is much older. So this essay follows the trace of the term 'Neoplatonism' from german philosophical historians, like Büsching and Brucker, back to the Cambridge Platonists and tries to demonstrate that the origin of the concept is based on some texts of the late antiquity which act first on the re…Read more
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247On the Origin of Venn DiagramsAxiomathes 32 (3): 887-900. 2022.In this paper we argue that there were several currents, ideas and problems in 19th-century logic that motivated John Venn to develop his famous logic diagrams. To this end, we first examine the problem of uncertainty or over-specification in syllogistic that became obvious in Euler diagrams. In the 19th century, numerous logicians tried to solve this problem. The most famous was the attempt to introduce dashed circles into Euler diagrams. The solution that John Venn developed for this problem, …Read more
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238Schopenhauers Logikdiagramme in den Mathematiklehrbüchern Adolph DiesterwegsSiegener Beiträge Zur Geschichte Und Philosophie der Mathematik 16 97-127. 2022.Ein Beispiel für die Rezeption und Fortführung der schopenhauerschen Logik findet man in den Mathematiklehrbüchern Friedrich Adolph Wilhelm Diesterwegs (1790–1866), In diesem Aufsatz werden die historische und systematische Dimension dieser Anwendung von Logikdiagramme auf die Mathematik skizziert. In Kapitel 2 wird zunächst die frühe Rezeption der schopenhauerschen Logik und Philosophie der Mathematik vorgestellt. Dabei werden einige oftmals tradierte Vorurteile, die das Werk Schopenhauers betr…Read more
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237ショーペンハウアーにおける意味の使用理論と文脈原理 : ヴィトゲンシュタインショーペンハウアー研究 = Schopenhauer-Studien 22 150-190. 2017.Japanese translation of ""Schopenhauers Gebrauchstheorie der Bedeutung und das Kontextprinzip. Eine Parallele zu Wittgensteins Philosophischen Untersuchungen". In: 97. Schopenhauer-Jahrbuch (2016), S. 29–51" by Tadahiro Oota (太田 匡洋 [訳])
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202Does Logic Have a History at All?Foundations of Science 1-23. forthcoming.To believe that logic has no history might at first seem peculiar today. But since the early 20th century, this position has been repeatedly conflated with logical monism of Kantian provenance. This logical monism asserts that only one logic is authoritative, thereby rendering all other research in the field marginal and negating the possibility of acknowledging a history of logic. In this paper, I will show how this and many related issues have developed, and that they are founded on only one p…Read more
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193Can Non-Causal Explanations Answer the Leibniz Question?Metaphysica 23 (2): 427-443. 2022.Leibniz is often cited as an authority when it comes to the formulation and answer strategy of the question “Why is there something rather than nothing?” Yet much current research assumes that Leibniz advocates an unambiguous question and strategy for the answer. In this respect, one repeatedly finds the argument in the literature that alternative explanatory approaches to this question violate Leibniz’s intention, since he derives the question from the principle of sufficient reason and also de…Read more
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113Seneca’s and Porphyry’s Trees in Modern InterpretationIn Jens Lemanski & Ingolf Max (eds.), Historia Logicae and its Modern Interpretation, College Publications. pp. 61-87. 2023.This paper presents an analysis of Seneca's 58th letter to Lucilius and Porphyry's Isagoge, which were the origin of the tree diagrams that became popular in philosophy and logic from the early Middle Ages onwards. These diagrams visualise the extent to which a concept can be understood as a category, genus, species or individual and what the method of dihairesis (division) means. The paper explores the dissimilarities between Seneca's and Porphyry's tree structures, scrutinising them through th…Read more
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86A Diagrammatic Representation of Hegel’s Science of LogicIn Viana P. Manalo E. Legg C. Linker S. Stapleton G. Basu A. (ed.), Diagrams 2021: Diagrammatic Representation and Inference, Springer. pp. 255-259. 2021.In this paper, we interpret a 19th century diagram, which is meant to visualise G.W.F. Hegel’s entire method of the `Science of Logic' on the basis of bitwise operations. For the interpretation of the diagram we use a binary numeral system, and discuss whether the anti-Hegelian argument associated with it is valid or not. The reinterpretation is intended to make more precise rules of construction, a stricter binary code and a review of strengths and weaknesses of the critique.
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77Oppositional Geometry in the Diagrammatic Calculus CLSouth American Journal of Logic 3 (2): 517-531. 2017.The paper presents the diagrammatic calculus CL, which combines features of tree, Euler-type, Venn-type diagrams and squares of opposition. In its basic form, `CL' (= Cubus Logicus) organizes terms in the form of a square or cube. By applying the arrows of the square of opposition to CL, judgments and inferences can be displayed. Thus CL offers on the one hand an intuitive method to display ontologies and on the other hand a diagrammatic tool to check inferences. The paper focuses mainly on the …Read more
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69Calculus CL as a Formal SystemIn Ahti Veikko Pietarinen, Peter Chapman, Leonie Bosveld-de Smet, Valeria Giardino, James Corter & Sven Linker (eds.), Diagrammatic Representation and Inference. Diagrams 2020. Lecture Notes in Computer Science, vol 12169. 2020., . pp. 445-460. 2020.In recent years CL diagrams inspired by Lange’s Cubus Logicus have been used in various contexts of diagrammatic reasoning. However, whether CL diagrams can also be used as a formal system seemed questionable. We present a CL diagram as a formal system, which is a fragment of propositional logic. Syntax and semantics are presented separately and a variant of bitstring semantics is applied to prove soundness and completeness of the system.
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64Language, Logic, and Mathematics in Schopenhauer (edited book)Birkhäuser. 2020.The chapters in this timely volume aim to answer the growing interest in Arthur Schopenhauer’s logic, mathematics, and philosophy of language by comprehensively exploring his work on mathematical evidence, logic diagrams, and problems of semantics. Thus, this work addresses the lack of research on these subjects in the context of Schopenhauer’s oeuvre by exposing their links to modern research areas, such as the “proof without words” movement, analytic philosophy and diagrammatic reasoning, demo…Read more
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63Problems and interpretations of Schopenhauer’s World as Will and RepresentationVoluntas: Revista Internacional de Filosofia 10 (1): 199-211. 2019.In this paper we present an overview of the current interpretations of the first volume of Arthur Schopenhauer’s main work The World as Will and Representation (W I) and discuss their problems. We discuss four issues, which in our opinion must clarify a current interpretation implicitly or explicitly, if it claims to be an interpretation of the whole book: (1) What does Schopenhauer mean by the fact that his work shares only one (single) thought? (2) How are the individual books of W I related? …Read more
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63Arthur Schopenhauer: Logic and DialecticInternet Encyclopedia of Philosophy. 2023.For Arthur Schopenhauer (1788-1860), logic as a discipline belongs to the human faculty of reason, more precisely to the faculty of language. This discipline of logic breaks down into two areas. Logic or analytics is one side of the coin; dialectic or the art of persuasion is the other. The former investigates rule-oriented and monological language. The latter investigates result-oriented language and persuasive language...
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